If $cos^4 α − sin^4α =\frac{5}{6}$, then the value of $2 cos^2 α − 1$ = − − − − − − − − − −

$\frac{5}{6}$

cos4 α - sin4 α = \(\frac{5}{6}\)

( cos²α - sin²α ) . ( cos²α + sin²α ) = \(\frac{5}{6}\)

{ using , cos²α + sin²α = 1 }

( cos²α - sin²α ) = \(\frac{5}{6}\)

Add and subtract cos²α.

( cos²α + cos²α - sin²α - cos²α  ) = \(\frac{5}{6}\)

( 2cos²α - 1  ) = \(\frac{5}{6}\)